We study the mitigation of climate tipping point transitions using an energy balance model. The evolution of the global mean surface temperature is coupled with the CO2 concentration through the green house effect. We model the CO2 concentration with a stochastic delay differential equation (SDDE), accounting for various carbon emission and capture scenarios. The resulting coupled system of SDDEs exhibits a tipping point phenomena: if CO2 concentration exceeds a critical threshold (around 478ppm), the temperature experiences an abrupt increase of about six degrees Celsius. We show that the CO2 concentration exhibits a transient growth which may cause a climate tipping point, even if the concentration decays asymptotically. We derive a rigorous upper bound for the CO2 evolution which quantifies its transient and asymptotic growths, and provides sufficient conditions for evading the climate tipping point. Combining this upper bound with Monte Carlo simulations of the stochastic climate model, we investigate the emission reduction and carbon capture scenarios that would avert the tipping point.
Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We consider an underlying potential, as defined theoretically for a saddle-node fold and (via averaging) for a Hopf bifurcation. Close to a stable state, this potential has a parabolic form; but approaching a jump it becomes increasingly dominated by softening nonlinearities. If we have already detec…
It is often known, from modelling studies, that a certain mode of climate tipping (of the oceanic thermohaline circulation, for example) is governed by an underlying fold bifurcation. For such a case we present a scheme of analysis that determines the best stochastic fit to the existing data. This provides the evolution rate of the effective control parameter, the variation of the stability coefficient, the path itself and its tipping point. By assessing the actual effective level of noise in the available time series, we are then able to make probability estimates of the time of tipping. This…
A climate state close to a tipping point will have a degenerate linear response to perturbations, which can be associated with extreme values of the equilibrium climate sensitivity (ECS). In this paper we contrast linearized (`instantaneous') with fully nonlinear geometric (`two-point') notions of ECS, in both presence and absence of tipping points. For a stochastic energy balance model of the global mean surface temperature with two stable regimes, we confirm that tipping events cause the appearance of extremes in both notions of ECS. Moreover, multiple regimes with different mean sensitiviti…
Climate response metrics are used to quantify the Earth's climate response to anthropogenic changes of atmospheric CO2. Equilibrium Climate Sensitivity (ECS) is one such metric that measures the equilibrium response to CO2 doubling. However, both in their estimation and their usage, such metrics make assumptions on the linearity of climate response, although it is known that, especially for larger forcing levels, response can be nonlinear. Such nonlinear responses may become visible immediately in response to a larger perturbation, or may only become apparent after a long transient. In this pa…
In ecology, climate and other fields, (sub)systems have been identified that can transition into a qualitatively different state when a critical threshold or tipping point in a driving process is crossed. An understanding of those tipping elements is of great interest given the increasing influence of humans on the biophysical Earth system. Complex interactions exist between tipping elements, e.g. physical mechanisms connect subsystems of the climate system. Based on earlier work on such coupled nonlinear systems, we systematically assessed the qualitative long-term behaviour of interacting ti…
ClimTip-GML: A global bias-corrected and downscaled dataset for assessing impacts of climate tipping events
Technical University of Munich（慕尼黑工业大学）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Ludwig-Maximilians University of Munich（慕尼黑路德维希-马克西米利安大学）；Met Office（英国气象局）；Utrecht University（乌得勒支大学）；University of Exeter（埃克塞特大学）
University of Victoria（维多利亚大学）；Palo Alto Research Center（帕洛阿尔托研究中心）；Excarta；University of California San Diego（加利福尼亚大学圣迭戈分校）；University of Washington（华盛顿大学）
Marine cloud brightening (MCB) is a proposed climate intervention technology to partially offset greenhouse gas warming and possibly avoid crossing climate tipping points. The impacts of MCB on regional climate are typically estimated using computationally expensive Earth System Model (ESM) simulations, preventing a thorough assessment of the large possibility space of potential MCB interventions. Here, we describe an AI model, named AiBEDO, that can be used to rapidly projects climate responses to forcings via a novel application of the Fluctuation-Dissipation Theorem (FDT). AiBEDO is a Multi…
Dansgaard-Oeschger events are a prominent mode of variability in the records of the last glacial cycle. Various prototype models have been proposed to explain these rapid climate fluctuations, and no agreement has emerged on which may be the more correct for describing the paleoclimatic signal. In this work, we assess the bimodality of the system reconstructing the topology of the multi--dimensional attractor over which the climate system evolves. We use high-resolution ice core isotope data to investigate the statistical properties of the climate fluctuations in the period before the onset of…
Many climate subsystems are thought to be susceptible to tipping - and some might be close to a tipping point. The general belief and intuition, based on simple conceptual models of tipping elements, is that tipping leads to reorganization of the full (sub)system. Here, we explore tipping in conceptual, but spatially extended and spatially heterogenous models. These are extensions of conceptual models taken from all sorts of climate system components on multiple spatial scales. By analysis of the bifurcation structure of such systems, special stable equilibrium states are revealed: coexistence…
Several environmental tipping points and self-reinforcing feedback loops are still disregarded within the frequently used climate models. Thus, existing climate models are not very representative for providing projections of the conditions after the actual environmental tipping points are triggered. In this contribution, we discuss the presence of the Arctic sea-ice loss tipping point and its influence on global warming. Our literature search and PIOMAS sea volume observation data based projection indicate the significant acceleration of the sea-ice loss (which leads to a year around and perma…
Current techniques for predicting climate change are mainly based on "massive" deterministic numerical modeling. However, the ocean-atmosphere system is a so-called "complex system", made up of a large number of interacting elements. We show that, in such systems, owing to the particularly large sensitivity to initial conditions, the approach of a possible tipping over a critical point cannot be evidenced "by construction" using numerical modeling, due to the divergence of computation time in the vicinity of the tipping point. On the other hand, the increasing amplitudes of observed climatic i…
Using in a simple way the theory of non linear dynamical systems, we show that increasing climatic instabilities may be a qualitative warning sign for the occurrence of a nearby bifurcation, yielding a discontinuous and sudden climate tipping towards an unknown and unpredictable state. The possibility of an accurate prediction of the occurrence time of such a transition is also discussed in terms of the approach of a critical point.
The variation in the Arctic sea ice is dominated by the seasonal cycle with little inter-annual correlation. Though the mean sea ice area has decreased steadily in the period of satellite observations, a dramatic transition in the dynamics was initiated with the record low September ice area in 2007. The change is much more pronounced in the amplitude of the seasonal cycle than in the annual mean ice area. The shape of the seasonal cycle is surprisingly constant for the whole observational record despite the general decline. A simple explanation, independent of the increased greenhouse warming…
Abrupt and irreversible winter Arctic sea-ice loss may occur under anthropogenic warming due to the collapse of a sea-ice equilibrium at a threshold value of CO$_2$, commonly referred to as a tipping point. Previous work has been unable to conclusively identify whether a tipping point in Arctic sea ice exists because fully-coupled climate models are too computationally expensive to run to equilibrium for many CO$_2$ values. Here, we explore the deviation of sea ice from its equilibrium state under realistic rates of CO$_2$ increase to demonstrate how a few time-dependent CO$_2$ experiments can…
University of Waterloo（滑铁卢大学）；University of Exeter（埃克塞特大学）；Wageningen University（瓦赫宁根大学）；McGill University（麦吉尔大学）；University of Guelph（圭尔夫大学）
The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is quite difficult. This has led to the development of an alternative suite of methods that seek to identify signatures of critical phenomena in data, which are expected to occur in advance of many classes of dynamical bifurcation. Crucially, the manifestations of these critical phenomena are generic across a variety of systems, meaning that data-intensive deep le…
We revisit a recent claim that the Earth's climate system is characterized by sensitive dependence to parameters; in particular, that the system exhibits an asymmetric, large-amplitude response to normally distributed feedback forcing. Such a response would imply irreducible uncertainty in climate change predictions and thus have notable implications for climate science and climate-related policy making. We show that equilibrium climate sensitivity in all generality does not support such an intrinsic indeterminacy; the latter appears only in essentially linear systems. The main flaw in the ana…
Climate network characterization of the AMOC edge state
University of Geneva（日内瓦大学）；Centre pour la Vie dans l’Univers (CVU)（宇宙生命中心）；Institute for Marine and Atmospheric research Utrecht（乌得勒支海洋与大气研究所）；Utrecht University（乌得勒支大学）；School of Computing and Mathematical Sciences, University of Leicester（莱斯特大学计算与数学科学学院）；Schools of Sciences, Great Bay University（大湾区大学理学院）
Machine-learning prediction of tipping with applications to the Atlantic Meridional Overturning Circulation
School of Electrical, Computer, and Energy Engineering, Arizona State University（亚利桑那州立大学电气、计算机与能源工程学院）；Army Research Directorate, DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室陆军研究局）；Department of Physics, Arizona State University（亚利桑那州立大学物理系）
Global warming due to human-made gases, mainly CO2, is already 0.8°C and deleterious climate impacts are growing worldwide. More warming is 'in the pipeline' because Earth is out of energy balance, with absorbed solar energy exceeding planetary heat radiation. Maintaining a climate that resembles the Holocene, the world of stable shorelines in which civilization developed, requires rapidly reducing fossil fuel CO2 emissions. Such a scenario is economically sensible and has multiple benefits for humanity and other species. Yet fossil fuel extraction is expanding, including highly carbon-intensi…
In our modeling of the long-term carbon cycle we find potential multiple steady-states in Phanerozoic climates. We include the effects of biotic enhancement of weathering on land, organic carbon burial, oxidation of reduced organic carbon in terrestrial sediments and the variation of biotic productivity with temperature, finding a second stable steady-state appearing between 20 and 50 oC. The very warm early Triassic climate as well as an oceanic anoxic event in the late Cretaceous may be the potential candidates for an upper temperature steady-state. Given our results, the anthropogenic drive…
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks wi…
Recent analyses indicate that the amount of atmospheric CO2 required to cause dangerous climate change is at most 450 ppm, and likely less than that. Reductions of non-CO2 climate forcings can provide only moderate, albeit important, adjustments to the CO2 limit. Realization of how close the planet is to "tipping points" with unacceptable consequences, especially ice sheet disintegration with sea level rise out of humanity's control, has a bright side. It implies an imperative: we must find a way to keep the CO2 amount so low that it will also avert other detrimental effects that had begun to …
Amazon forest dieback is seen as a potential tipping point under climate change. These concerns are partly based-on an early coupled climate-carbon cycle simulation, that produced unusually strong drying and warming in Amazonia. In contrast, the 5th generation Earth System Models (CMIP5) produced few examples of Amazon dieback under climate change. Here we examine results from seven 6th generation models (CMIP6) which include vegetation dynamics, and in some cases interactive forest fires. Although these models typically project increases in area-mean forest carbon across Amazonia under CO2-in…
Investigating the Robustness of Extreme Precipitation Super-Resolution Across Climates
Expertise Center for Climate Extremes, University of Lausanne（极端气候专家中心，洛桑大学）；Faculty of Geosciences and Environment, University of Lausanne（地球科学与环境学院，洛桑大学）；Faculty of Business and Economics (HEC), University of Lausanne（商业经济学院（HEC），洛桑大学）
Climate change is a reality of today. Paleoclimatic proxies and climate predictions based on coupled atmosphere-ocean general circulation models provide us with temperature data. Using Detrended Fluctuation Analysis, we are investigating the statistical connection between the climate types of the present and these local temperatures. We are relating this issue to some well-known historic climate shifts. Our main result is that the temperature fluctuations with or without a temperature scale attached to them, can be used to classify climates in the absence of other indicators such as pan evapor…
Tropospheric ozone (O3) is a greenhouse gas which can absorb heat and make the weather even hotter during extreme heatwaves. Besides, it is an influential ground-level air pollutant which can severely damage the environment. Thus evaluating the importance of various factors related to the O3 formation process is essential. However, O3 simulated by the available climate models exhibits large variance in different places, indicating the insufficiency of models in explaining the O3 formation process correctly. In this paper, we aim to identify and understand the impact of various factors on O3 fo…
Field measurement campaigns have grown exponentially in recent years, stemming from the need for reliable data to validate urban climate models and obtain a better understanding of urban climate features. Also contributing to this growth is the Local Climate Zone (LCZ) scheme, firstly developed to enhance the accuracy in the contextualisation of urban measurements, and lately used for characterising urban areas. Due to its relative novelty, researchers are still investigating the potential of LCZs and its indicators for urban temperature variability detection. In this respect, the present stud…
Tropical cyclones remain a major threat to the lives, property and economy of communities around the South West Indian ocean (SWIO), notably Southern Africa and Madagascar. This study uses the weather research forecast (WRF) model to perform a series of simulations for tropical cyclone Enawo with the aim of investigating the effect of an increase or decrease (by 2$^{\circ}C$) in sea surface temperature (SST) on the intensity of the tropical cyclone (using windspeed, precipitation and pressure as measures of cyclone intensity). The experiment uses the data from European Centre for Medium-Range …
